Valuation model for catastrophe reinsurance contracts covering multiple insurance products: An application to Indonesian earthquake data

Catastrophes, like earthquakes, bring sudden and severe damage, causing fatalities, injuries, and property loss. This often triggers a rapid increase in insurance claims. These claims can encompass various types, such as life insurance claims for deaths, health insurance claims for injuries, and general insurance claims for property damage. For insurers offering multiple types of coverage, this surge in claims can pose a risk of financial losses or bankruptcy. One option for insurers is to transfer some of these risks to reinsurance companies. Reinsurance companies will assess the potential losses due to a catastrophe event, then issue catastrophe reinsurance contracts to insurance companies. This study aims to construct a valuation model for catastrophe reinsurance contracts that can cover claim losses arising from two types of insurance products. Valuation in this study is done using the Fundamental Theorem of Asset Pricing, which is the expected present value of the number of claims that occur during the reinsurance coverage period. The number of catastrophe events during the reinsurance coverage period is assumed to follow a Poisson process. Each impact of a catastrophe event, such as the number of fatalities and injuries that cause claims, is represented as random variables, and modeled using Peaks Over Threshold (POT). This study uses Clayton, Gumbel, and Frank copulas to describe various dependence characteristics between random variables. The parameters of the POT model and copula are estimated using Inference Functions for Margins method. After estimating the model parameters, Monte Carlo simulations are performed to obtain numerical solutions for the expected value of catastrophe reinsurance based on the Fundamental Theorem of Asset Pricing. The expected reinsurance value based on Monte Carlo simulations using Indonesian earthquake data from 1979–2021 is Rp 10,296,819,838.